#18620: Galois conjugates in universal cyclotomic field miss the previously
existing parameter m
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Reporter: stumpc5 | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.8
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by stumpc5):
Hi,
you might be right in the sense that you will see the same elements
multiple times or the same elements in a different order such as
{{{
sage: zeta.galois_conjugates(5)
[E(5), E(5)^2, E(5)^3, E(5)^4]
sage: zeta.galois_conjugates(10)
[E(5), E(5)^3, E(5)^2, E(5)^4]
sage: zeta.galois_conjugates(15)
[E(5), E(5)^2, E(5)^4, E(5)^2, E(5)^3, E(5), E(5)^3, E(5)^4]
}}}
You can argue that these elements live in the {{{UCF}}} so their Galois
conjugates should be computed using {{{UCF/QQ}}}. But since every such
element is contained in {{{CF(n)}}} for multiple {{{n}}}s, one can as well
argue to compute it in one of those (recall that the Galois conjugates are
defined over a field extension
http://en.wikipedia.org/wiki/Conjugate_element_%28field_theory%29).
The orbit **as a set** does not depend on your choice above, but the order
in which they come in the list depends on the field extension {{{CF(n)}}}
you chose, and you might want to further use that ordering for something.
What I find more important is that you broke my code without providing a
workaround. And I am also not a big fan of the rudeness or at least
missing politeness that seems to become standard in SageMath discussions.
Christian
--
Ticket URL: <http://trac.sagemath.org/ticket/18620#comment:2>
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